Solved Uniform Circular Motion Problems Physics

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There are two forces acting on the block on the plane of the ground: the centerpointing applied force on the block, and friction.

In the film 2001: A Space Odyssey, a wheel like space station achieves artificial gravity by spinning around its axis.

If the station had a size of 2 km, how fast should it be spinning for the people inside to feel the same gravitational acceleration as on earth?

The sum of the forces on this plane is $$\sum = F_R - F_$$ By Newton's Second Law: $$ma = F_R - F_$$ Now we know the formula for the applied force: $$ma = \frac - F_$$ We also know the formula for the frictional force: $$ma = \frac - mg\mu_k$$ Divide away \(m\): $$a = \frac - g\mu_k$$ Now solve for \(R\): $$a R = v^2 - Rg\mu_k \Rightarrow$$ $$a R Rg\mu_k = v^2 \Rightarrow$$ $$R(a g\mu_k) = v^2 \Rightarrow$$ $$R = \frac$$ Feel free to check the units on the right-hand side to ensure they are units of length.

Now plug in the known values: $$R = \frac = 1.236 \; m$$ Example 4: A stone is rolling around in a uniform circular motion.

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